Problem: Graph this system of equations and solve. $-3x+y = -2$ $-x-y = -2$ 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 1 2 3 4 5 6 7 8 9 10 \llap{-}2 \llap{-}3 \llap{-}4 \llap{-}5 \llap{-}6 \llap{-}7 \llap{-}8 \llap{-}9 \llap{-}10 Click and drag the points to move the lines.
Convert the first equation, $-3x+y = -2$ , to slope-intercept form. $y = 3 x - 2$ The y-intercept for the first equation is $-2$ , so the first line must pass through the point $(0, -2)$ The slope for the first equation is $3$ . Remember that the slope tells you rise over run. So in this case for every $3$ positions you move up $1$ position to the right. $3$ positions up from $(0, -2)$ is $(1, 1)$ Graph the blue line so it passes through $(0, -2)$ and $(1, 1)$ Convert the second equation, $-x-y = -2$ , to slope-intercept form. $y = - x + 2$ The y-intercept for the second equation is $2$ , so the second line must pass through the point $(0, 2)$ The slope for the second equation is $-1$ . Remember that the slope tells you rise over run. So in this case for every $1$ position you move down (because it's negative) You must also move $1$ position to the right. $1$ position to the right. $1$ position down from $(0, 2)$ is $(1, 1)$ Graph the green line so it passes through $(0, 2)$ and $(1, 1)$ The solution is the point where the two lines intersect. The lines intersect at $(1, 1)$.